The generator matrix
1 1 1 1 1 1
0 3 6 0 3 6
generates a code of length 6 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+78x^12+2x^18
The gray image is a code over GF(3) with n=54, k=4 and d=36.
This code was found by Heurico 1.16 in 8.61e-005 seconds.